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GENERAL PHYSICS II
Electromagnetism
&
Thermal Physics
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Chapter IX
Conductors, Capacitors
§1. Charges and electric field on conductors
§2. Capacitance of conductors and capacitors
§3. Energy storage in capacitors and electric field energy
§4. Electric current, resistance and electromotive force
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§1. Charges and electric field on conductors:
1.1 The balance of charges on conductors:
In conductors there are charged particles which can be freely
move under any small force. Therefore the balance of charges on
conductors can be observed under these circumstances:
 The electric field equals zero everywhere inside the conductor
E = 0
The electric potential is constant inside the conductor
V = const
 The electric field vector on the surface of conductors direct along the
normal of the surface at each point
E = En
The surface of conductors is equipotential
 Inside conductors there is no charge. This conclusion can be proved
by applying the Gauss’s law for any arbitrary closed surface inside
conductor. All the charge is distributed on the surface of conductors.
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 Since the distribution of charge on conductors

rare E is smaller
the charge density is small
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§2. Capacitance of conductors and capacitors:
2.1 Charging by induction:
A charge body (rod) can give
another body a charge of
opposite sign, without losing
any of its own charge.
Pictures:
a) Metal sphere is initially uncharged
b) Charged rod brought nearby
c) Wire allows piled-up electrons to
flow to ground
d) Wire is disconnected from sphere
e) Charged rod is removed: Electrons
on sphere rearrange themselves.
Metal sphere
Isulating
stand
Negatively
charged
rod
a)
b)
c)
d)
e)
wire
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C 
 Need Q:
 Need V: from definition:
 Use Gauss’ Law to find E (in next slide)
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Recall the formula for the electric field of two infinite sheets:
• Field outside the sheets is zero
Gaussian surface encloses zero net
charge
E=0
E=0
E

+
+
+
+
+
+
+

+
+
+
-
-
-
-
-
-

A
Q
E 
d
A
Q
EdldEVV
b
a
ab
0






d
A
V
Q
C
0


Remark:
• The capacitance of this capacitor depends only on its shape and size
• This formula is true for parallel-plate capacitor (shape), and C depends
on A, d (size) (for another shape one has other formula).
• When the space between the metal plates is filled with a dielectric